Ovals with 4n Centres: The Ground Plan of the Colosseum and the Neuilly Bridge Arches

Abstract

Ovals with more than four centres have been widely used, for example to align important points in a building and/or to improve a four-centre oval in its resemblance to an ellipse. These can be so close to each other that many researchers argue whether famous buildings were in fact designed (and/or built) as eight (or more) -centre ovals or as ellipses. Within the common work on the Colosseum [1], Trevisan (see [18]) compares the ground plan of various Roman amphitheatres and discusses the four- and eight-centre options (we will discuss this in detail in Sect. 8.2), while Benedetti (see [2]) suggests an eight-centre oval construction for Antonio da Sangallo’s Vatican dome, as also reported by Migliari in [12], where in general the oval vs ellipse dispute is discussed. Due to technical, practical and aesthetical advantages, arches and bridges have often been built using half-ovals with 5, 7, 9 or more centres (the formula for a half-oval is 2n + 1 centres): we will deal with an example of this in Sect. 8.3—the bridge at Neuilly by Perronet—with the help of Zerlenga’s book [20]. More about lowered arches can then be found in Breymann’s work [3].